Properties

Label 225.4.h.d.181.16
Level $225$
Weight $4$
Character 225.181
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.16
Character \(\chi\) \(=\) 225.181
Dual form 225.4.h.d.46.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71061 + 5.26471i) q^{2} +(-18.3188 + 13.3094i) q^{4} +(11.1283 - 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 - 47.6460i) q^{8} +O(q^{10})\) \(q+(1.71061 + 5.26471i) q^{2} +(-18.3188 + 13.3094i) q^{4} +(11.1283 - 1.07706i) q^{5} -30.2200 q^{7} +(-65.5791 - 47.6460i) q^{8} +(24.7066 + 56.7450i) q^{10} +(6.53575 + 20.1150i) q^{11} +(-1.85672 + 5.71440i) q^{13} +(-51.6946 - 159.100i) q^{14} +(82.6849 - 254.478i) q^{16} +(-17.3999 - 12.6418i) q^{17} +(-85.2864 - 61.9642i) q^{19} +(-189.523 + 167.842i) q^{20} +(-94.7194 + 68.8177i) q^{22} +(-1.91808 - 5.90324i) q^{23} +(122.680 - 23.9717i) q^{25} -33.2608 q^{26} +(553.596 - 402.211i) q^{28} +(-187.176 + 135.991i) q^{29} +(142.099 + 103.241i) q^{31} +832.711 q^{32} +(36.7909 - 113.231i) q^{34} +(-336.299 + 32.5487i) q^{35} +(-90.6084 + 278.864i) q^{37} +(180.332 - 555.004i) q^{38} +(-781.104 - 459.589i) q^{40} +(-18.2039 + 56.0257i) q^{41} -379.656 q^{43} +(-387.446 - 281.496i) q^{44} +(27.7978 - 20.1962i) q^{46} +(131.812 - 95.7671i) q^{47} +570.251 q^{49} +(336.061 + 604.868i) q^{50} +(-42.0424 - 129.393i) q^{52} +(-214.314 + 155.708i) q^{53} +(94.3971 + 216.807i) q^{55} +(1981.80 + 1439.87i) q^{56} +(-1036.14 - 752.798i) q^{58} +(141.788 - 436.378i) q^{59} +(185.460 + 570.786i) q^{61} +(-300.457 + 924.713i) q^{62} +(762.963 + 2348.16i) q^{64} +(-14.5075 + 65.5916i) q^{65} +(-269.638 - 195.903i) q^{67} +487.002 q^{68} +(-746.635 - 1714.84i) q^{70} +(-715.330 + 519.718i) q^{71} +(100.853 + 310.394i) q^{73} -1623.13 q^{74} +2387.05 q^{76} +(-197.511 - 607.876i) q^{77} +(-63.7800 + 46.3389i) q^{79} +(646.058 - 2920.97i) q^{80} -326.099 q^{82} +(-1062.34 - 771.834i) q^{83} +(-207.248 - 121.941i) q^{85} +(-649.442 - 1998.78i) q^{86} +(529.790 - 1630.53i) q^{88} +(348.484 + 1072.52i) q^{89} +(56.1102 - 172.690i) q^{91} +(113.706 + 82.6120i) q^{92} +(729.664 + 530.132i) q^{94} +(-1015.83 - 597.700i) q^{95} +(40.0395 - 29.0904i) q^{97} +(975.476 + 3002.21i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.71061 + 5.26471i 0.604791 + 1.86136i 0.498220 + 0.867050i \(0.333987\pi\)
0.106571 + 0.994305i \(0.466013\pi\)
\(3\) 0 0
\(4\) −18.3188 + 13.3094i −2.28986 + 1.66368i
\(5\) 11.1283 1.07706i 0.995349 0.0963350i
\(6\) 0 0
\(7\) −30.2200 −1.63173 −0.815865 0.578243i \(-0.803739\pi\)
−0.815865 + 0.578243i \(0.803739\pi\)
\(8\) −65.5791 47.6460i −2.89822 2.10568i
\(9\) 0 0
\(10\) 24.7066 + 56.7450i 0.781292 + 1.79444i
\(11\) 6.53575 + 20.1150i 0.179146 + 0.551354i 0.999799 0.0200732i \(-0.00638993\pi\)
−0.820653 + 0.571427i \(0.806390\pi\)
\(12\) 0 0
\(13\) −1.85672 + 5.71440i −0.0396125 + 0.121915i −0.968907 0.247424i \(-0.920416\pi\)
0.929295 + 0.369339i \(0.120416\pi\)
\(14\) −51.6946 159.100i −0.986855 3.03723i
\(15\) 0 0
\(16\) 82.6849 254.478i 1.29195 3.97622i
\(17\) −17.3999 12.6418i −0.248241 0.180358i 0.456706 0.889618i \(-0.349029\pi\)
−0.704947 + 0.709260i \(0.749029\pi\)
\(18\) 0 0
\(19\) −85.2864 61.9642i −1.02979 0.748187i −0.0615244 0.998106i \(-0.519596\pi\)
−0.968267 + 0.249918i \(0.919596\pi\)
\(20\) −189.523 + 167.842i −2.11893 + 1.87653i
\(21\) 0 0
\(22\) −94.7194 + 68.8177i −0.917920 + 0.666908i
\(23\) −1.91808 5.90324i −0.0173890 0.0535178i 0.941985 0.335654i \(-0.108957\pi\)
−0.959374 + 0.282136i \(0.908957\pi\)
\(24\) 0 0
\(25\) 122.680 23.9717i 0.981439 0.191774i
\(26\) −33.2608 −0.250884
\(27\) 0 0
\(28\) 553.596 402.211i 3.73642 2.71467i
\(29\) −187.176 + 135.991i −1.19854 + 0.870791i −0.994140 0.108097i \(-0.965524\pi\)
−0.204400 + 0.978887i \(0.565524\pi\)
\(30\) 0 0
\(31\) 142.099 + 103.241i 0.823280 + 0.598148i 0.917650 0.397389i \(-0.130084\pi\)
−0.0943701 + 0.995537i \(0.530084\pi\)
\(32\) 832.711 4.60012
\(33\) 0 0
\(34\) 36.7909 113.231i 0.185576 0.571144i
\(35\) −336.299 + 32.5487i −1.62414 + 0.157193i
\(36\) 0 0
\(37\) −90.6084 + 278.864i −0.402592 + 1.23905i 0.520296 + 0.853986i \(0.325821\pi\)
−0.922889 + 0.385066i \(0.874179\pi\)
\(38\) 180.332 555.004i 0.769834 2.36930i
\(39\) 0 0
\(40\) −781.104 459.589i −3.08759 1.81668i
\(41\) −18.2039 + 56.0257i −0.0693406 + 0.213408i −0.979722 0.200362i \(-0.935788\pi\)
0.910381 + 0.413770i \(0.135788\pi\)
\(42\) 0 0
\(43\) −379.656 −1.34644 −0.673220 0.739442i \(-0.735089\pi\)
−0.673220 + 0.739442i \(0.735089\pi\)
\(44\) −387.446 281.496i −1.32749 0.964480i
\(45\) 0 0
\(46\) 27.7978 20.1962i 0.0890990 0.0647342i
\(47\) 131.812 95.7671i 0.409080 0.297214i −0.364149 0.931341i \(-0.618640\pi\)
0.773229 + 0.634127i \(0.218640\pi\)
\(48\) 0 0
\(49\) 570.251 1.66254
\(50\) 336.061 + 604.868i 0.950525 + 1.71082i
\(51\) 0 0
\(52\) −42.0424 129.393i −0.112120 0.345069i
\(53\) −214.314 + 155.708i −0.555440 + 0.403551i −0.829787 0.558080i \(-0.811538\pi\)
0.274347 + 0.961631i \(0.411538\pi\)
\(54\) 0 0
\(55\) 94.3971 + 216.807i 0.231427 + 0.531532i
\(56\) 1981.80 + 1439.87i 4.72910 + 3.43589i
\(57\) 0 0
\(58\) −1036.14 752.798i −2.34572 1.70426i
\(59\) 141.788 436.378i 0.312868 0.962908i −0.663755 0.747950i \(-0.731038\pi\)
0.976623 0.214958i \(-0.0689616\pi\)
\(60\) 0 0
\(61\) 185.460 + 570.786i 0.389273 + 1.19806i 0.933333 + 0.359013i \(0.116887\pi\)
−0.544059 + 0.839047i \(0.683113\pi\)
\(62\) −300.457 + 924.713i −0.615454 + 1.89417i
\(63\) 0 0
\(64\) 762.963 + 2348.16i 1.49016 + 4.58625i
\(65\) −14.5075 + 65.5916i −0.0276836 + 0.125164i
\(66\) 0 0
\(67\) −269.638 195.903i −0.491665 0.357215i 0.314160 0.949370i \(-0.398277\pi\)
−0.805824 + 0.592155i \(0.798277\pi\)
\(68\) 487.002 0.868494
\(69\) 0 0
\(70\) −746.635 1714.84i −1.27486 2.92803i
\(71\) −715.330 + 519.718i −1.19569 + 0.868721i −0.993854 0.110698i \(-0.964691\pi\)
−0.201838 + 0.979419i \(0.564691\pi\)
\(72\) 0 0
\(73\) 100.853 + 310.394i 0.161698 + 0.497656i 0.998778 0.0494250i \(-0.0157389\pi\)
−0.837080 + 0.547081i \(0.815739\pi\)
\(74\) −1623.13 −2.54980
\(75\) 0 0
\(76\) 2387.05 3.60281
\(77\) −197.511 607.876i −0.292317 0.899661i
\(78\) 0 0
\(79\) −63.7800 + 46.3389i −0.0908330 + 0.0659940i −0.632275 0.774744i \(-0.717879\pi\)
0.541442 + 0.840738i \(0.317879\pi\)
\(80\) 646.058 2920.97i 0.902894 4.08218i
\(81\) 0 0
\(82\) −326.099 −0.439165
\(83\) −1062.34 771.834i −1.40490 1.02072i −0.994039 0.109023i \(-0.965228\pi\)
−0.410862 0.911698i \(-0.634772\pi\)
\(84\) 0 0
\(85\) −207.248 121.941i −0.264462 0.155605i
\(86\) −649.442 1998.78i −0.814315 2.50620i
\(87\) 0 0
\(88\) 529.790 1630.53i 0.641770 1.97517i
\(89\) 348.484 + 1072.52i 0.415047 + 1.27738i 0.912209 + 0.409726i \(0.134376\pi\)
−0.497161 + 0.867658i \(0.665624\pi\)
\(90\) 0 0
\(91\) 56.1102 172.690i 0.0646368 0.198932i
\(92\) 113.706 + 82.6120i 0.128855 + 0.0936184i
\(93\) 0 0
\(94\) 729.664 + 530.132i 0.800629 + 0.581691i
\(95\) −1015.83 597.700i −1.09708 0.645502i
\(96\) 0 0
\(97\) 40.0395 29.0904i 0.0419113 0.0304503i −0.566632 0.823971i \(-0.691754\pi\)
0.608544 + 0.793520i \(0.291754\pi\)
\(98\) 975.476 + 3002.21i 1.00549 + 3.09458i
\(99\) 0 0
\(100\) −1928.30 + 2071.93i −1.92830 + 2.07193i
\(101\) −790.998 −0.779279 −0.389640 0.920967i \(-0.627400\pi\)
−0.389640 + 0.920967i \(0.627400\pi\)
\(102\) 0 0
\(103\) 46.4033 33.7140i 0.0443908 0.0322518i −0.565369 0.824838i \(-0.691266\pi\)
0.609759 + 0.792587i \(0.291266\pi\)
\(104\) 394.031 286.280i 0.371518 0.269924i
\(105\) 0 0
\(106\) −1186.37 861.946i −1.08708 0.789808i
\(107\) −470.946 −0.425496 −0.212748 0.977107i \(-0.568241\pi\)
−0.212748 + 0.977107i \(0.568241\pi\)
\(108\) 0 0
\(109\) −71.2432 + 219.264i −0.0626042 + 0.192676i −0.977467 0.211090i \(-0.932299\pi\)
0.914863 + 0.403765i \(0.132299\pi\)
\(110\) −979.949 + 867.845i −0.849404 + 0.752234i
\(111\) 0 0
\(112\) −2498.74 + 7690.33i −2.10811 + 6.48811i
\(113\) −54.7705 + 168.566i −0.0455962 + 0.140331i −0.971263 0.238009i \(-0.923505\pi\)
0.925667 + 0.378340i \(0.123505\pi\)
\(114\) 0 0
\(115\) −27.7032 63.6274i −0.0224638 0.0515938i
\(116\) 1618.88 4982.40i 1.29577 3.98797i
\(117\) 0 0
\(118\) 2539.95 1.98153
\(119\) 525.827 + 382.036i 0.405063 + 0.294295i
\(120\) 0 0
\(121\) 714.905 519.409i 0.537119 0.390240i
\(122\) −2687.77 + 1952.78i −1.99459 + 1.44915i
\(123\) 0 0
\(124\) −3977.16 −2.88032
\(125\) 1339.40 398.899i 0.958400 0.285429i
\(126\) 0 0
\(127\) −250.813 771.924i −0.175245 0.539348i 0.824400 0.566008i \(-0.191513\pi\)
−0.999645 + 0.0266600i \(0.991513\pi\)
\(128\) −5667.82 + 4117.91i −3.91382 + 2.84356i
\(129\) 0 0
\(130\) −370.137 + 35.8238i −0.249717 + 0.0241689i
\(131\) 1053.96 + 765.747i 0.702938 + 0.510714i 0.880888 0.473325i \(-0.156946\pi\)
−0.177950 + 0.984040i \(0.556946\pi\)
\(132\) 0 0
\(133\) 2577.36 + 1872.56i 1.68034 + 1.22084i
\(134\) 570.130 1754.68i 0.367550 1.13120i
\(135\) 0 0
\(136\) 538.741 + 1658.08i 0.339682 + 1.04543i
\(137\) 343.611 1057.53i 0.214282 0.659493i −0.784922 0.619595i \(-0.787297\pi\)
0.999204 0.0398976i \(-0.0127032\pi\)
\(138\) 0 0
\(139\) 7.34441 + 22.6038i 0.00448162 + 0.0137930i 0.953272 0.302112i \(-0.0976918\pi\)
−0.948791 + 0.315905i \(0.897692\pi\)
\(140\) 5727.40 5072.20i 3.45753 3.06199i
\(141\) 0 0
\(142\) −3959.81 2876.97i −2.34014 1.70021i
\(143\) −127.080 −0.0743146
\(144\) 0 0
\(145\) −1936.49 + 1714.96i −1.10908 + 0.982202i
\(146\) −1461.62 + 1061.93i −0.828521 + 0.601956i
\(147\) 0 0
\(148\) −2051.68 6314.41i −1.13950 3.50703i
\(149\) 2190.65 1.20446 0.602232 0.798321i \(-0.294278\pi\)
0.602232 + 0.798321i \(0.294278\pi\)
\(150\) 0 0
\(151\) 891.600 0.480513 0.240256 0.970709i \(-0.422769\pi\)
0.240256 + 0.970709i \(0.422769\pi\)
\(152\) 2640.66 + 8127.11i 1.40912 + 4.33681i
\(153\) 0 0
\(154\) 2862.42 2079.67i 1.49780 1.08821i
\(155\) 1692.52 + 995.850i 0.877074 + 0.516055i
\(156\) 0 0
\(157\) 2339.90 1.18946 0.594728 0.803927i \(-0.297260\pi\)
0.594728 + 0.803927i \(0.297260\pi\)
\(158\) −353.063 256.515i −0.177773 0.129160i
\(159\) 0 0
\(160\) 9266.69 896.878i 4.57873 0.443153i
\(161\) 57.9644 + 178.396i 0.0283741 + 0.0873266i
\(162\) 0 0
\(163\) −687.964 + 2117.34i −0.330586 + 1.01744i 0.638270 + 0.769813i \(0.279650\pi\)
−0.968856 + 0.247626i \(0.920350\pi\)
\(164\) −412.196 1268.61i −0.196263 0.604035i
\(165\) 0 0
\(166\) 2246.24 6913.21i 1.05025 3.23234i
\(167\) −501.922 364.668i −0.232574 0.168975i 0.465394 0.885103i \(-0.345913\pi\)
−0.697969 + 0.716128i \(0.745913\pi\)
\(168\) 0 0
\(169\) 1748.20 + 1270.14i 0.795723 + 0.578127i
\(170\) 287.466 1299.70i 0.129692 0.586366i
\(171\) 0 0
\(172\) 6954.85 5052.99i 3.08315 2.24004i
\(173\) 774.704 + 2384.29i 0.340461 + 1.04783i 0.963969 + 0.266013i \(0.0857066\pi\)
−0.623509 + 0.781816i \(0.714293\pi\)
\(174\) 0 0
\(175\) −3707.39 + 724.427i −1.60144 + 0.312923i
\(176\) 5659.23 2.42375
\(177\) 0 0
\(178\) −5050.40 + 3669.33i −2.12665 + 1.54510i
\(179\) −1412.93 + 1026.56i −0.589987 + 0.428651i −0.842311 0.538992i \(-0.818805\pi\)
0.252324 + 0.967643i \(0.418805\pi\)
\(180\) 0 0
\(181\) 275.217 + 199.957i 0.113020 + 0.0821142i 0.642860 0.765984i \(-0.277748\pi\)
−0.529839 + 0.848098i \(0.677748\pi\)
\(182\) 1005.14 0.409374
\(183\) 0 0
\(184\) −155.480 + 478.518i −0.0622942 + 0.191722i
\(185\) −707.968 + 3200.88i −0.281356 + 1.27207i
\(186\) 0 0
\(187\) 140.568 432.623i 0.0549697 0.169179i
\(188\) −1140.04 + 3508.68i −0.442266 + 1.36115i
\(189\) 0 0
\(190\) 1409.02 6370.50i 0.538006 2.43245i
\(191\) 754.426 2321.89i 0.285803 0.879611i −0.700354 0.713796i \(-0.746974\pi\)
0.986157 0.165815i \(-0.0530256\pi\)
\(192\) 0 0
\(193\) −2643.56 −0.985946 −0.492973 0.870045i \(-0.664090\pi\)
−0.492973 + 0.870045i \(0.664090\pi\)
\(194\) 221.644 + 161.034i 0.0820264 + 0.0595957i
\(195\) 0 0
\(196\) −10446.3 + 7589.71i −3.80698 + 2.76593i
\(197\) 2093.75 1521.20i 0.757225 0.550156i −0.140833 0.990033i \(-0.544978\pi\)
0.898058 + 0.439877i \(0.144978\pi\)
\(198\) 0 0
\(199\) 772.004 0.275005 0.137502 0.990501i \(-0.456093\pi\)
0.137502 + 0.990501i \(0.456093\pi\)
\(200\) −9187.40 4273.16i −3.24824 1.51079i
\(201\) 0 0
\(202\) −1353.09 4164.37i −0.471301 1.45052i
\(203\) 5656.46 4109.66i 1.95569 1.42089i
\(204\) 0 0
\(205\) −142.236 + 643.080i −0.0484594 + 0.219096i
\(206\) 256.872 + 186.628i 0.0868792 + 0.0631215i
\(207\) 0 0
\(208\) 1300.67 + 944.990i 0.433582 + 0.315016i
\(209\) 688.997 2120.52i 0.228033 0.701814i
\(210\) 0 0
\(211\) 1842.83 + 5671.63i 0.601257 + 1.85048i 0.520718 + 0.853729i \(0.325664\pi\)
0.0805394 + 0.996751i \(0.474336\pi\)
\(212\) 1853.60 5704.80i 0.600499 1.84815i
\(213\) 0 0
\(214\) −805.603 2479.39i −0.257336 0.791998i
\(215\) −4224.94 + 408.911i −1.34018 + 0.129709i
\(216\) 0 0
\(217\) −4294.23 3119.94i −1.34337 0.976016i
\(218\) −1276.23 −0.396501
\(219\) 0 0
\(220\) −4614.82 2715.28i −1.41423 0.832110i
\(221\) 104.547 75.9580i 0.0318217 0.0231198i
\(222\) 0 0
\(223\) 1435.00 + 4416.46i 0.430917 + 1.32623i 0.897213 + 0.441597i \(0.145588\pi\)
−0.466297 + 0.884628i \(0.654412\pi\)
\(224\) −25164.6 −7.50615
\(225\) 0 0
\(226\) −981.143 −0.288782
\(227\) 418.007 + 1286.49i 0.122221 + 0.376156i 0.993384 0.114836i \(-0.0366343\pi\)
−0.871164 + 0.490992i \(0.836634\pi\)
\(228\) 0 0
\(229\) 2577.13 1872.40i 0.743675 0.540312i −0.150185 0.988658i \(-0.547987\pi\)
0.893860 + 0.448346i \(0.147987\pi\)
\(230\) 287.590 254.690i 0.0824484 0.0730165i
\(231\) 0 0
\(232\) 18754.3 5.30723
\(233\) −1720.35 1249.91i −0.483708 0.351434i 0.319052 0.947737i \(-0.396636\pi\)
−0.802759 + 0.596303i \(0.796636\pi\)
\(234\) 0 0
\(235\) 1363.70 1207.70i 0.378545 0.335240i
\(236\) 3210.55 + 9881.05i 0.885546 + 2.72543i
\(237\) 0 0
\(238\) −1111.82 + 3421.84i −0.302810 + 0.931953i
\(239\) 1449.47 + 4461.01i 0.392295 + 1.20736i 0.931049 + 0.364895i \(0.118895\pi\)
−0.538754 + 0.842463i \(0.681105\pi\)
\(240\) 0 0
\(241\) −1069.17 + 3290.58i −0.285774 + 0.879522i 0.700391 + 0.713759i \(0.253009\pi\)
−0.986166 + 0.165763i \(0.946991\pi\)
\(242\) 3957.46 + 2875.26i 1.05122 + 0.763756i
\(243\) 0 0
\(244\) −10994.2 7987.78i −2.88456 2.09576i
\(245\) 6345.95 614.194i 1.65481 0.160161i
\(246\) 0 0
\(247\) 512.442 372.311i 0.132008 0.0959091i
\(248\) −4399.70 13540.9i −1.12654 3.46712i
\(249\) 0 0
\(250\) 4391.28 + 6369.22i 1.11092 + 1.61130i
\(251\) 5528.48 1.39026 0.695128 0.718886i \(-0.255348\pi\)
0.695128 + 0.718886i \(0.255348\pi\)
\(252\) 0 0
\(253\) 106.207 77.1642i 0.0263921 0.0191750i
\(254\) 3634.91 2640.92i 0.897932 0.652386i
\(255\) 0 0
\(256\) −15395.3 11185.4i −3.75862 2.73080i
\(257\) 2290.19 0.555869 0.277934 0.960600i \(-0.410350\pi\)
0.277934 + 0.960600i \(0.410350\pi\)
\(258\) 0 0
\(259\) 2738.19 8427.28i 0.656922 2.02180i
\(260\) −607.226 1394.65i −0.144841 0.332663i
\(261\) 0 0
\(262\) −2228.52 + 6858.68i −0.525491 + 1.61729i
\(263\) 651.760 2005.91i 0.152811 0.470304i −0.845122 0.534574i \(-0.820472\pi\)
0.997933 + 0.0642705i \(0.0204720\pi\)
\(264\) 0 0
\(265\) −2217.26 + 1963.61i −0.513981 + 0.455182i
\(266\) −5449.64 + 16772.3i −1.25616 + 3.86606i
\(267\) 0 0
\(268\) 7546.82 1.72013
\(269\) −6952.97 5051.63i −1.57595 1.14499i −0.921162 0.389180i \(-0.872758\pi\)
−0.654787 0.755814i \(-0.727242\pi\)
\(270\) 0 0
\(271\) 3304.58 2400.92i 0.740734 0.538175i −0.152207 0.988349i \(-0.548638\pi\)
0.892941 + 0.450174i \(0.148638\pi\)
\(272\) −4655.77 + 3382.61i −1.03786 + 0.754048i
\(273\) 0 0
\(274\) 6155.35 1.35715
\(275\) 1284.00 + 2311.03i 0.281556 + 0.506765i
\(276\) 0 0
\(277\) −1157.41 3562.16i −0.251055 0.772669i −0.994581 0.103962i \(-0.966848\pi\)
0.743526 0.668707i \(-0.233152\pi\)
\(278\) −106.439 + 77.3324i −0.0229632 + 0.0166838i
\(279\) 0 0
\(280\) 23605.0 + 13888.8i 5.03810 + 2.96434i
\(281\) −3085.22 2241.55i −0.654978 0.475870i 0.209985 0.977705i \(-0.432658\pi\)
−0.864963 + 0.501835i \(0.832658\pi\)
\(282\) 0 0
\(283\) −2689.86 1954.30i −0.565003 0.410499i 0.268284 0.963340i \(-0.413544\pi\)
−0.833287 + 0.552841i \(0.813544\pi\)
\(284\) 6186.88 19041.3i 1.29269 3.97849i
\(285\) 0 0
\(286\) −217.384 669.040i −0.0449448 0.138326i
\(287\) 550.121 1693.10i 0.113145 0.348225i
\(288\) 0 0
\(289\) −1375.26 4232.61i −0.279922 0.861512i
\(290\) −12341.3 7261.42i −2.49899 1.47036i
\(291\) 0 0
\(292\) −5978.68 4343.77i −1.19820 0.870547i
\(293\) −6316.24 −1.25938 −0.629691 0.776846i \(-0.716818\pi\)
−0.629691 + 0.776846i \(0.716818\pi\)
\(294\) 0 0
\(295\) 1107.86 5008.88i 0.218651 0.988570i
\(296\) 19228.8 13970.5i 3.77584 2.74331i
\(297\) 0 0
\(298\) 3747.34 + 11533.1i 0.728449 + 2.24193i
\(299\) 37.2948 0.00721343
\(300\) 0 0
\(301\) 11473.2 2.19703
\(302\) 1525.18 + 4694.02i 0.290610 + 0.894405i
\(303\) 0 0
\(304\) −22820.4 + 16580.0i −4.30539 + 3.12805i
\(305\) 2678.63 + 6152.15i 0.502878 + 1.15499i
\(306\) 0 0
\(307\) −8592.04 −1.59731 −0.798655 0.601790i \(-0.794455\pi\)
−0.798655 + 0.601790i \(0.794455\pi\)
\(308\) 11708.6 + 8506.82i 2.16611 + 1.57377i
\(309\) 0 0
\(310\) −2347.62 + 10614.1i −0.430116 + 1.94465i
\(311\) −140.125 431.260i −0.0255490 0.0786319i 0.937469 0.348069i \(-0.113162\pi\)
−0.963018 + 0.269437i \(0.913162\pi\)
\(312\) 0 0
\(313\) −1961.96 + 6038.28i −0.354302 + 1.09043i 0.602112 + 0.798412i \(0.294326\pi\)
−0.956413 + 0.292016i \(0.905674\pi\)
\(314\) 4002.65 + 12318.9i 0.719372 + 2.21400i
\(315\) 0 0
\(316\) 551.632 1697.75i 0.0982017 0.302234i
\(317\) −5897.27 4284.62i −1.04487 0.759143i −0.0736400 0.997285i \(-0.523462\pi\)
−0.971230 + 0.238142i \(0.923462\pi\)
\(318\) 0 0
\(319\) −3958.79 2876.23i −0.694827 0.504822i
\(320\) 11019.6 + 25309.4i 1.92505 + 4.42136i
\(321\) 0 0
\(322\) −840.049 + 610.332i −0.145385 + 0.105629i
\(323\) 700.639 + 2156.35i 0.120695 + 0.371462i
\(324\) 0 0
\(325\) −90.7984 + 745.551i −0.0154972 + 0.127248i
\(326\) −12324.0 −2.09375
\(327\) 0 0
\(328\) 3863.19 2806.77i 0.650333 0.472494i
\(329\) −3983.37 + 2894.09i −0.667508 + 0.484973i
\(330\) 0 0
\(331\) −3531.10 2565.49i −0.586365 0.426019i 0.254648 0.967034i \(-0.418040\pi\)
−0.841013 + 0.541015i \(0.818040\pi\)
\(332\) 29733.5 4.91517
\(333\) 0 0
\(334\) 1061.28 3266.28i 0.173864 0.535098i
\(335\) −3211.62 1889.66i −0.523790 0.308189i
\(336\) 0 0
\(337\) 663.043 2040.64i 0.107176 0.329853i −0.883059 0.469262i \(-0.844520\pi\)
0.990235 + 0.139408i \(0.0445201\pi\)
\(338\) −3696.45 + 11376.5i −0.594853 + 1.83077i
\(339\) 0 0
\(340\) 5419.52 524.529i 0.864455 0.0836664i
\(341\) −1147.96 + 3533.07i −0.182304 + 0.561075i
\(342\) 0 0
\(343\) −6867.55 −1.08109
\(344\) 24897.5 + 18089.1i 3.90227 + 2.83517i
\(345\) 0 0
\(346\) −11227.4 + 8157.18i −1.74448 + 1.26744i
\(347\) −6185.75 + 4494.21i −0.956970 + 0.695279i −0.952445 0.304710i \(-0.901440\pi\)
−0.00452493 + 0.999990i \(0.501440\pi\)
\(348\) 0 0
\(349\) 7655.39 1.17416 0.587082 0.809527i \(-0.300276\pi\)
0.587082 + 0.809527i \(0.300276\pi\)
\(350\) −10155.8 18279.1i −1.55100 2.79160i
\(351\) 0 0
\(352\) 5442.39 + 16750.0i 0.824093 + 2.53630i
\(353\) 5076.69 3688.43i 0.765453 0.556134i −0.135125 0.990829i \(-0.543144\pi\)
0.900578 + 0.434694i \(0.143144\pi\)
\(354\) 0 0
\(355\) −7400.67 + 6554.05i −1.10644 + 0.979867i
\(356\) −20658.5 15009.3i −3.07555 2.23452i
\(357\) 0 0
\(358\) −7821.50 5682.65i −1.15469 0.838931i
\(359\) −2156.39 + 6636.67i −0.317019 + 0.975683i 0.657897 + 0.753108i \(0.271446\pi\)
−0.974916 + 0.222575i \(0.928554\pi\)
\(360\) 0 0
\(361\) 1314.66 + 4046.10i 0.191669 + 0.589897i
\(362\) −581.926 + 1790.98i −0.0844899 + 0.260033i
\(363\) 0 0
\(364\) 1270.52 + 3910.27i 0.182949 + 0.563060i
\(365\) 1456.64 + 3345.55i 0.208888 + 0.479764i
\(366\) 0 0
\(367\) −1972.27 1432.94i −0.280522 0.203811i 0.438623 0.898671i \(-0.355466\pi\)
−0.719145 + 0.694860i \(0.755466\pi\)
\(368\) −1660.84 −0.235264
\(369\) 0 0
\(370\) −18062.8 + 1748.21i −2.53794 + 0.245635i
\(371\) 6476.59 4705.52i 0.906328 0.658486i
\(372\) 0 0
\(373\) 697.469 + 2146.59i 0.0968193 + 0.297979i 0.987724 0.156212i \(-0.0499283\pi\)
−0.890904 + 0.454191i \(0.849928\pi\)
\(374\) 2518.09 0.348148
\(375\) 0 0
\(376\) −13207.0 −1.81144
\(377\) −429.575 1322.10i −0.0586850 0.180614i
\(378\) 0 0
\(379\) 7532.09 5472.38i 1.02084 0.741682i 0.0543834 0.998520i \(-0.482681\pi\)
0.966454 + 0.256838i \(0.0826807\pi\)
\(380\) 26564.0 2571.00i 3.58606 0.347077i
\(381\) 0 0
\(382\) 13514.6 1.81012
\(383\) −5295.40 3847.33i −0.706481 0.513289i 0.175555 0.984470i \(-0.443828\pi\)
−0.882037 + 0.471181i \(0.843828\pi\)
\(384\) 0 0
\(385\) −2852.68 6551.92i −0.377627 0.867316i
\(386\) −4522.09 13917.6i −0.596291 1.83520i
\(387\) 0 0
\(388\) −346.301 + 1065.80i −0.0453112 + 0.139454i
\(389\) −1760.54 5418.39i −0.229468 0.706230i −0.997807 0.0661869i \(-0.978917\pi\)
0.768339 0.640043i \(-0.221083\pi\)
\(390\) 0 0
\(391\) −41.2531 + 126.964i −0.00533570 + 0.0164216i
\(392\) −37396.6 27170.2i −4.81840 3.50077i
\(393\) 0 0
\(394\) 11590.2 + 8420.80i 1.48200 + 1.07674i
\(395\) −659.856 + 584.369i −0.0840530 + 0.0744375i
\(396\) 0 0
\(397\) 7305.74 5307.93i 0.923589 0.671026i −0.0208261 0.999783i \(-0.506630\pi\)
0.944415 + 0.328757i \(0.106630\pi\)
\(398\) 1320.60 + 4064.38i 0.166320 + 0.511881i
\(399\) 0 0
\(400\) 4043.50 33201.4i 0.505437 4.15018i
\(401\) −1291.00 −0.160772 −0.0803859 0.996764i \(-0.525615\pi\)
−0.0803859 + 0.996764i \(0.525615\pi\)
\(402\) 0 0
\(403\) −853.797 + 620.320i −0.105535 + 0.0766758i
\(404\) 14490.2 10527.7i 1.78444 1.29647i
\(405\) 0 0
\(406\) 31312.1 + 22749.6i 3.82758 + 2.78090i
\(407\) −6201.53 −0.755279
\(408\) 0 0
\(409\) −1299.63 + 3999.85i −0.157121 + 0.483570i −0.998370 0.0570792i \(-0.981821\pi\)
0.841248 + 0.540649i \(0.181821\pi\)
\(410\) −3628.94 + 351.227i −0.437123 + 0.0423070i
\(411\) 0 0
\(412\) −401.341 + 1235.20i −0.0479919 + 0.147704i
\(413\) −4284.83 + 13187.4i −0.510515 + 1.57121i
\(414\) 0 0
\(415\) −12653.4 7445.03i −1.49670 0.880632i
\(416\) −1546.11 + 4758.45i −0.182222 + 0.560822i
\(417\) 0 0
\(418\) 12342.5 1.44424
\(419\) 4482.54 + 3256.76i 0.522641 + 0.379721i 0.817598 0.575790i \(-0.195305\pi\)
−0.294957 + 0.955510i \(0.595305\pi\)
\(420\) 0 0
\(421\) 5750.48 4177.97i 0.665704 0.483662i −0.202881 0.979203i \(-0.565030\pi\)
0.868584 + 0.495541i \(0.165030\pi\)
\(422\) −26707.1 + 19403.9i −3.08077 + 2.23831i
\(423\) 0 0
\(424\) 21473.4 2.45953
\(425\) −2437.67 1133.79i −0.278222 0.129404i
\(426\) 0 0
\(427\) −5604.60 17249.2i −0.635188 1.95491i
\(428\) 8627.18 6268.01i 0.974323 0.707887i
\(429\) 0 0
\(430\) −9380.00 21543.6i −1.05196 2.41610i
\(431\) 4596.49 + 3339.54i 0.513701 + 0.373225i 0.814226 0.580549i \(-0.197162\pi\)
−0.300525 + 0.953774i \(0.597162\pi\)
\(432\) 0 0
\(433\) 12267.7 + 8913.00i 1.36154 + 0.989218i 0.998345 + 0.0575050i \(0.0183145\pi\)
0.363196 + 0.931713i \(0.381685\pi\)
\(434\) 9079.84 27944.9i 1.00425 3.09078i
\(435\) 0 0
\(436\) −1613.18 4964.87i −0.177196 0.545353i
\(437\) −202.203 + 622.318i −0.0221343 + 0.0681224i
\(438\) 0 0
\(439\) 583.950 + 1797.21i 0.0634861 + 0.195390i 0.977769 0.209687i \(-0.0672446\pi\)
−0.914282 + 0.405077i \(0.867245\pi\)
\(440\) 4139.51 18715.7i 0.448508 2.02780i
\(441\) 0 0
\(442\) 578.736 + 420.476i 0.0622798 + 0.0452489i
\(443\) −14518.3 −1.55707 −0.778536 0.627600i \(-0.784037\pi\)
−0.778536 + 0.627600i \(0.784037\pi\)
\(444\) 0 0
\(445\) 5033.22 + 11560.1i 0.536174 + 1.23146i
\(446\) −20796.7 + 15109.7i −2.20796 + 1.60418i
\(447\) 0 0
\(448\) −23056.8 70961.5i −2.43154 7.48351i
\(449\) −15727.5 −1.65307 −0.826535 0.562885i \(-0.809691\pi\)
−0.826535 + 0.562885i \(0.809691\pi\)
\(450\) 0 0
\(451\) −1245.93 −0.130086
\(452\) −1240.19 3816.90i −0.129056 0.397194i
\(453\) 0 0
\(454\) −6057.96 + 4401.37i −0.626243 + 0.454992i
\(455\) 438.417 1982.18i 0.0451721 0.204233i
\(456\) 0 0
\(457\) −3024.30 −0.309564 −0.154782 0.987949i \(-0.549468\pi\)
−0.154782 + 0.987949i \(0.549468\pi\)
\(458\) 14266.1 + 10364.9i 1.45548 + 1.05747i
\(459\) 0 0
\(460\) 1354.33 + 796.867i 0.137274 + 0.0807698i
\(461\) −1738.63 5350.95i −0.175653 0.540604i 0.824010 0.566576i \(-0.191732\pi\)
−0.999663 + 0.0259714i \(0.991732\pi\)
\(462\) 0 0
\(463\) −1365.98 + 4204.05i −0.137111 + 0.421985i −0.995912 0.0903241i \(-0.971210\pi\)
0.858801 + 0.512309i \(0.171210\pi\)
\(464\) 19130.1 + 58876.5i 1.91400 + 5.89068i
\(465\) 0 0
\(466\) 3637.55 11195.2i 0.361602 1.11290i
\(467\) 4026.97 + 2925.76i 0.399028 + 0.289911i 0.769145 0.639075i \(-0.220682\pi\)
−0.370117 + 0.928985i \(0.620682\pi\)
\(468\) 0 0
\(469\) 8148.47 + 5920.21i 0.802263 + 0.582878i
\(470\) 8690.94 + 5113.60i 0.852942 + 0.501857i
\(471\) 0 0
\(472\) −30090.0 + 21861.7i −2.93433 + 2.13192i
\(473\) −2481.34 7636.76i −0.241209 0.742365i
\(474\) 0 0
\(475\) −11948.3 5557.30i −1.15416 0.536813i
\(476\) −14717.2 −1.41715
\(477\) 0 0
\(478\) −21006.4 + 15262.1i −2.01007 + 1.46040i
\(479\) −5836.76 + 4240.66i −0.556761 + 0.404511i −0.830272 0.557358i \(-0.811815\pi\)
0.273511 + 0.961869i \(0.411815\pi\)
\(480\) 0 0
\(481\) −1425.31 1035.55i −0.135111 0.0981639i
\(482\) −19152.9 −1.80994
\(483\) 0 0
\(484\) −6183.20 + 19029.9i −0.580692 + 1.78718i
\(485\) 414.241 366.852i 0.0387829 0.0343462i
\(486\) 0 0
\(487\) 4846.33 14915.5i 0.450941 1.38785i −0.424894 0.905243i \(-0.639689\pi\)
0.875835 0.482610i \(-0.160311\pi\)
\(488\) 15033.4 46268.0i 1.39453 4.29192i
\(489\) 0 0
\(490\) 14089.0 + 32358.9i 1.29893 + 2.98332i
\(491\) 4177.42 12856.8i 0.383960 1.18171i −0.553271 0.833001i \(-0.686621\pi\)
0.937232 0.348707i \(-0.113379\pi\)
\(492\) 0 0
\(493\) 4976.02 0.454581
\(494\) 2836.69 + 2060.98i 0.258358 + 0.187708i
\(495\) 0 0
\(496\) 38021.9 27624.5i 3.44200 2.50076i
\(497\) 21617.3 15705.9i 1.95104 1.41752i
\(498\) 0 0
\(499\) −19053.5 −1.70932 −0.854660 0.519188i \(-0.826234\pi\)
−0.854660 + 0.519188i \(0.826234\pi\)
\(500\) −19227.2 + 25134.1i −1.71974 + 2.24806i
\(501\) 0 0
\(502\) 9457.05 + 29105.8i 0.840815 + 2.58776i
\(503\) −12244.1 + 8895.89i −1.08537 + 0.788565i −0.978611 0.205720i \(-0.934046\pi\)
−0.106756 + 0.994285i \(0.534046\pi\)
\(504\) 0 0
\(505\) −8802.49 + 851.950i −0.775655 + 0.0750719i
\(506\) 587.926 + 427.153i 0.0516532 + 0.0375282i
\(507\) 0 0
\(508\) 14868.5 + 10802.6i 1.29859 + 0.943478i
\(509\) 2000.14 6155.78i 0.174174 0.536052i −0.825421 0.564518i \(-0.809062\pi\)
0.999595 + 0.0284660i \(0.00906222\pi\)
\(510\) 0 0
\(511\) −3047.79 9380.13i −0.263848 0.812040i
\(512\) 15233.0 46882.2i 1.31486 4.04672i
\(513\) 0 0
\(514\) 3917.62 + 12057.2i 0.336185 + 1.03467i
\(515\) 480.080 425.160i 0.0410774 0.0363782i
\(516\) 0 0
\(517\) 2787.84 + 2025.49i 0.237155 + 0.172303i
\(518\) 49051.1 4.16059
\(519\) 0 0
\(520\) 4076.57 3610.22i 0.343787 0.304459i
\(521\) −12414.6 + 9019.77i −1.04395 + 0.758471i −0.971052 0.238869i \(-0.923223\pi\)
−0.0728937 + 0.997340i \(0.523223\pi\)
\(522\) 0 0
\(523\) −1899.57 5846.27i −0.158819 0.488795i 0.839709 0.543037i \(-0.182726\pi\)
−0.998528 + 0.0542423i \(0.982726\pi\)
\(524\) −29499.0 −2.45929
\(525\) 0 0
\(526\) 11675.5 0.967821
\(527\) −1167.36 3592.77i −0.0964915 0.296970i
\(528\) 0 0
\(529\) 9812.14 7128.94i 0.806455 0.585924i
\(530\) −14130.7 8314.24i −1.15811 0.681411i
\(531\) 0 0
\(532\) −72136.9 −5.87882
\(533\) −286.354 208.048i −0.0232709 0.0169073i
\(534\) 0 0
\(535\) −5240.84 + 507.236i −0.423517 + 0.0409901i
\(536\) 8348.60 + 25694.4i 0.672770 + 2.07057i
\(537\) 0 0
\(538\) 14701.6 45246.7i 1.17812 3.62588i
\(539\) 3727.02 + 11470.6i 0.297837 + 0.916648i
\(540\) 0 0
\(541\) −3280.78 + 10097.2i −0.260724 + 0.802425i 0.731924 + 0.681386i \(0.238623\pi\)
−0.992648 + 0.121039i \(0.961377\pi\)
\(542\) 18293.0 + 13290.6i 1.44972 + 1.05329i
\(543\) 0 0
\(544\) −14489.1 10527.0i −1.14194 0.829669i
\(545\) −556.658 + 2516.78i −0.0437516 + 0.197811i
\(546\) 0 0
\(547\) −16829.3 + 12227.2i −1.31548 + 0.955754i −0.315506 + 0.948924i \(0.602174\pi\)
−0.999977 + 0.00683023i \(0.997826\pi\)
\(548\) 7780.50 + 23945.9i 0.606508 + 1.86664i
\(549\) 0 0
\(550\) −9970.49 + 10713.1i −0.772987 + 0.830563i
\(551\) 24390.1 1.88576
\(552\) 0 0
\(553\) 1927.43 1400.36i 0.148215 0.107684i
\(554\) 16773.8 12186.9i 1.28637 0.934606i
\(555\) 0 0
\(556\) −435.384 316.325i −0.0332094 0.0241280i
\(557\) 8938.79 0.679980 0.339990 0.940429i \(-0.389576\pi\)
0.339990 + 0.940429i \(0.389576\pi\)
\(558\) 0 0
\(559\) 704.915 2169.51i 0.0533358 0.164151i
\(560\) −19523.9 + 88271.9i −1.47328 + 6.66102i
\(561\) 0 0
\(562\) 6523.48 20077.2i 0.489638 1.50695i
\(563\) 3016.21 9282.93i 0.225787 0.694900i −0.772424 0.635107i \(-0.780956\pi\)
0.998211 0.0597931i \(-0.0190441\pi\)
\(564\) 0 0
\(565\) −427.949 + 1934.85i −0.0318654 + 0.144071i
\(566\) 5687.52 17504.4i 0.422375 1.29994i
\(567\) 0 0
\(568\) 71673.2 5.29462
\(569\) 11079.9 + 8050.05i 0.816336 + 0.593103i 0.915661 0.401952i \(-0.131668\pi\)
−0.0993244 + 0.995055i \(0.531668\pi\)
\(570\) 0 0
\(571\) 9324.33 6774.52i 0.683382 0.496506i −0.191096 0.981571i \(-0.561204\pi\)
0.874478 + 0.485065i \(0.161204\pi\)
\(572\) 2327.96 1691.36i 0.170170 0.123635i
\(573\) 0 0
\(574\) 9854.71 0.716599
\(575\) −376.820 678.229i −0.0273296 0.0491897i
\(576\) 0 0
\(577\) 4919.30 + 15140.0i 0.354927 + 1.09235i 0.956052 + 0.293198i \(0.0947195\pi\)
−0.601125 + 0.799155i \(0.705280\pi\)
\(578\) 19930.9 14480.7i 1.43429 1.04207i
\(579\) 0 0
\(580\) 12649.1 57189.5i 0.905562 4.09425i
\(581\) 32103.9 + 23324.9i 2.29242 + 1.66554i
\(582\) 0 0
\(583\) −4532.78 3293.26i −0.322004 0.233950i
\(584\) 8175.19 25160.6i 0.579267 1.78280i
\(585\) 0 0
\(586\) −10804.6 33253.2i −0.761663 2.34416i
\(587\) 5556.96 17102.6i 0.390733 1.20255i −0.541502 0.840700i \(-0.682144\pi\)
0.932235 0.361853i \(-0.117856\pi\)
\(588\) 0 0
\(589\) −5721.86 17610.1i −0.400280 1.23194i
\(590\) 28265.4 2735.67i 1.97232 0.190891i
\(591\) 0 0
\(592\) 63472.7 + 46115.6i 4.40661 + 3.20159i
\(593\) −230.646 −0.0159721 −0.00798607 0.999968i \(-0.502542\pi\)
−0.00798607 + 0.999968i \(0.502542\pi\)
\(594\) 0 0
\(595\) 6263.05 + 3685.08i 0.431530 + 0.253905i
\(596\) −40130.2 + 29156.3i −2.75805 + 2.00384i
\(597\) 0 0
\(598\) 63.7968 + 196.346i 0.00436262 + 0.0134268i
\(599\) −11209.1 −0.764597 −0.382298 0.924039i \(-0.624867\pi\)
−0.382298 + 0.924039i \(0.624867\pi\)
\(600\) 0 0
\(601\) 8219.09 0.557843 0.278922 0.960314i \(-0.410023\pi\)
0.278922 + 0.960314i \(0.410023\pi\)
\(602\) 19626.2 + 60403.1i 1.32874 + 4.08945i
\(603\) 0 0
\(604\) −16333.1 + 11866.7i −1.10030 + 0.799418i
\(605\) 7396.28 6550.16i 0.497027 0.440168i
\(606\) 0 0
\(607\) 9305.08 0.622210 0.311105 0.950376i \(-0.399301\pi\)
0.311105 + 0.950376i \(0.399301\pi\)
\(608\) −71018.9 51598.3i −4.73717 3.44175i
\(609\) 0 0
\(610\) −27807.2 + 24626.1i −1.84570 + 1.63456i
\(611\) 302.513 + 931.040i 0.0200301 + 0.0616463i
\(612\) 0 0
\(613\) −2405.39 + 7403.03i −0.158487 + 0.487774i −0.998498 0.0547965i \(-0.982549\pi\)
0.840010 + 0.542571i \(0.182549\pi\)
\(614\) −14697.6 45234.6i −0.966038 2.97316i
\(615\) 0 0
\(616\) −16010.3 + 49274.6i −1.04720 + 3.22294i
\(617\) 745.708 + 541.789i 0.0486565 + 0.0353510i 0.611848 0.790976i \(-0.290427\pi\)
−0.563191 + 0.826327i \(0.690427\pi\)
\(618\) 0 0
\(619\) 6014.72 + 4369.95i 0.390553 + 0.283753i 0.765682 0.643219i \(-0.222402\pi\)
−0.375129 + 0.926972i \(0.622402\pi\)
\(620\) −44259.2 + 4283.63i −2.86692 + 0.277475i
\(621\) 0 0
\(622\) 2030.76 1475.43i 0.130910 0.0951117i
\(623\) −10531.2 32411.7i −0.677245 2.08435i
\(624\) 0 0
\(625\) 14475.7 5881.70i 0.926446 0.376429i
\(626\) −35145.9 −2.24395
\(627\) 0 0
\(628\) −42864.3 + 31142.7i −2.72368 + 1.97887i
\(629\) 5101.92 3706.76i 0.323413 0.234973i
\(630\) 0 0
\(631\) 5821.33 + 4229.44i 0.367264 + 0.266833i 0.756075 0.654485i \(-0.227114\pi\)
−0.388812 + 0.921317i \(0.627114\pi\)
\(632\) 6390.50 0.402216
\(633\) 0 0
\(634\) 12469.4 38376.7i 0.781106 2.40400i
\(635\) −3622.54 8320.09i −0.226388 0.519957i
\(636\) 0 0
\(637\) −1058.80 + 3258.65i −0.0658573 + 0.202688i
\(638\) 8370.58 25762.0i 0.519427 1.59863i
\(639\) 0 0
\(640\) −58638.2 + 51930.1i −3.62169 + 3.20737i
\(641\) 467.168 1437.79i 0.0287863 0.0885951i −0.935631 0.352979i \(-0.885169\pi\)
0.964417 + 0.264384i \(0.0851687\pi\)
\(642\) 0 0
\(643\) −22396.8 −1.37363 −0.686813 0.726834i \(-0.740991\pi\)
−0.686813 + 0.726834i \(0.740991\pi\)
\(644\) −3436.19 2496.54i −0.210256 0.152760i
\(645\) 0 0
\(646\) −10154.0 + 7377.32i −0.618428 + 0.449314i
\(647\) −1561.70 + 1134.64i −0.0948944 + 0.0689448i −0.634221 0.773152i \(-0.718679\pi\)
0.539326 + 0.842097i \(0.318679\pi\)
\(648\) 0 0
\(649\) 9704.42 0.586952
\(650\) −4080.43 + 797.319i −0.246227 + 0.0481130i
\(651\) 0 0
\(652\) −15577.8 47943.5i −0.935696 2.87978i
\(653\) −23581.3 + 17132.8i −1.41318 + 1.02674i −0.420333 + 0.907370i \(0.638087\pi\)
−0.992850 + 0.119368i \(0.961913\pi\)
\(654\) 0 0
\(655\) 12553.6 + 7386.31i 0.748868 + 0.440622i
\(656\) 12752.1 + 9264.95i 0.758973 + 0.551426i
\(657\) 0 0
\(658\) −22050.5 16020.6i −1.30641 0.949162i
\(659\) −5189.79 + 15972.5i −0.306776 + 0.944161i 0.672232 + 0.740341i \(0.265336\pi\)
−0.979008 + 0.203820i \(0.934664\pi\)
\(660\) 0 0
\(661\) 7008.62 + 21570.3i 0.412411 + 1.26927i 0.914546 + 0.404482i \(0.132548\pi\)
−0.502135 + 0.864789i \(0.667452\pi\)
\(662\) 7466.26 22978.8i 0.438345 1.34909i
\(663\) 0 0
\(664\) 32892.4 + 101232.i 1.92240 + 5.91654i
\(665\) 30698.6 + 18062.5i 1.79013 + 1.05329i
\(666\) 0 0
\(667\) 1161.81 + 844.102i 0.0674442 + 0.0490011i
\(668\) 14048.2 0.813682
\(669\) 0 0
\(670\) 4454.71 20140.7i 0.256866 1.16135i
\(671\) −10269.2 + 7461.03i −0.590818 + 0.429255i
\(672\) 0 0
\(673\) 1787.87 + 5502.51i 0.102403 + 0.315165i 0.989112 0.147163i \(-0.0470142\pi\)
−0.886709 + 0.462328i \(0.847014\pi\)
\(674\) 11877.6 0.678793
\(675\) 0 0
\(676\) −48929.9 −2.78391
\(677\) −2989.08 9199.45i −0.169690 0.522251i 0.829662 0.558267i \(-0.188533\pi\)
−0.999351 + 0.0360158i \(0.988533\pi\)
\(678\) 0 0
\(679\) −1209.99 + 879.113i −0.0683878 + 0.0496867i
\(680\) 7781.14 + 17871.4i 0.438813 + 1.00785i
\(681\) 0 0
\(682\) −20564.3 −1.15462
\(683\) 23680.4 + 17204.8i 1.32666 + 0.963872i 0.999823 + 0.0187892i \(0.00598113\pi\)
0.326832 + 0.945082i \(0.394019\pi\)
\(684\) 0 0
\(685\) 2684.80 12138.6i 0.149753 0.677068i
\(686\) −11747.7 36155.6i −0.653831 2.01229i
\(687\) 0 0
\(688\) −31391.8 + 96613.9i −1.73954 + 5.35374i
\(689\) −491.859 1513.79i −0.0271964 0.0837020i
\(690\) 0 0
\(691\) −6623.67 + 20385.6i −0.364654 + 1.12229i 0.585543 + 0.810642i \(0.300881\pi\)
−0.950197 + 0.311650i \(0.899119\pi\)
\(692\) −45925.3 33366.7i −2.52286 1.83296i
\(693\) 0 0
\(694\) −34242.1 24878.4i −1.87293 1.36076i
\(695\) 106.077 + 243.632i 0.00578952 + 0.0132971i
\(696\) 0 0
\(697\) 1025.01 744.714i 0.0557031 0.0404707i
\(698\) 13095.4 + 40303.4i 0.710124 + 2.18554i
\(699\) 0 0
\(700\) 58273.4 62613.9i 3.14647 3.38083i
\(701\) 16727.9 0.901292 0.450646 0.892703i \(-0.351194\pi\)
0.450646 + 0.892703i \(0.351194\pi\)
\(702\) 0 0
\(703\) 25007.2 18168.8i 1.34163 0.974751i
\(704\) −42246.6 + 30694.0i −2.26169 + 1.64321i
\(705\) 0 0
\(706\) 28102.7 + 20417.8i 1.49810 + 1.08844i
\(707\) 23904.0 1.27157
\(708\) 0 0
\(709\) −5241.61 + 16132.0i −0.277648 + 0.854514i 0.710858 + 0.703335i \(0.248307\pi\)
−0.988506 + 0.151178i \(0.951693\pi\)
\(710\) −47164.8 27751.0i −2.49305 1.46687i
\(711\) 0 0
\(712\) 28248.2 86939.0i 1.48686 4.57609i
\(713\) 336.898 1036.87i 0.0176956 0.0544614i
\(714\) 0 0
\(715\) −1414.19 + 136.873i −0.0739689 + 0.00715909i
\(716\) 12220.4 37610.7i 0.637848 1.96310i
\(717\) 0 0
\(718\) −38628.9 −2.00782
\(719\) −6363.32 4623.22i −0.330058 0.239801i 0.410397 0.911907i \(-0.365390\pi\)
−0.740455 + 0.672106i \(0.765390\pi\)
\(720\) 0 0
\(721\) −1402.31 + 1018.84i −0.0724338 + 0.0526262i
\(722\) −19052.7 + 13842.6i −0.982088 + 0.713529i
\(723\) 0 0
\(724\) −7702.96 −0.395412
\(725\) −19702.8 + 21170.3i −1.00930 + 1.08448i
\(726\) 0 0
\(727\) 2605.34 + 8018.41i 0.132912 + 0.409060i 0.995259 0.0972567i \(-0.0310068\pi\)
−0.862348 + 0.506316i \(0.831007\pi\)
\(728\) −11907.6 + 8651.40i −0.606217 + 0.440443i
\(729\) 0 0
\(730\) −15121.6 + 13391.7i −0.766679 + 0.678972i
\(731\) 6605.98 + 4799.53i 0.334242 + 0.242841i
\(732\) 0 0
\(733\) −17055.7 12391.7i −0.859435 0.624416i 0.0682959 0.997665i \(-0.478244\pi\)
−0.927731 + 0.373249i \(0.878244\pi\)
\(734\) 4170.22 12834.6i 0.209708 0.645414i
\(735\) 0 0
\(736\) −1597.21 4915.69i −0.0799915 0.246189i
\(737\) 2178.31 6704.14i 0.108872 0.335075i
\(738\) 0 0
\(739\) −1688.56 5196.84i −0.0840522 0.258686i 0.900194 0.435489i \(-0.143424\pi\)
−0.984246 + 0.176803i \(0.943424\pi\)
\(740\) −29632.7 68059.1i −1.47205 3.38095i
\(741\) 0 0
\(742\) 35852.1 + 26048.1i 1.77382 + 1.28875i
\(743\) 12400.7 0.612300 0.306150 0.951983i \(-0.400959\pi\)
0.306150 + 0.951983i \(0.400959\pi\)
\(744\) 0 0
\(745\) 24378.3 2359.46i 1.19886 0.116032i
\(746\) −10108.1 + 7343.95i −0.496090 + 0.360430i
\(747\) 0 0
\(748\) 3182.92 + 9796.03i 0.155587 + 0.478848i
\(749\) 14232.0 0.694293
\(750\) 0 0
\(751\) −29073.8 −1.41267 −0.706336 0.707876i \(-0.749653\pi\)
−0.706336 + 0.707876i \(0.749653\pi\)
\(752\) −13471.7 41461.7i −0.653276 2.01058i
\(753\) 0 0
\(754\) 6225.62 4523.18i 0.300694 0.218467i
\(755\) 9922.03 960.305i 0.478278 0.0462902i
\(756\) 0 0
\(757\) −17652.4 −0.847539 −0.423770 0.905770i \(-0.639293\pi\)
−0.423770 + 0.905770i \(0.639293\pi\)
\(758\) 41695.0 + 30293.2i 1.99793 + 1.45158i
\(759\) 0 0
\(760\) 38139.5 + 87597.1i 1.82035 + 4.18090i
\(761\) −9492.07 29213.6i −0.452151 1.39158i −0.874447 0.485121i \(-0.838776\pi\)
0.422296 0.906458i \(-0.361224\pi\)
\(762\) 0 0
\(763\) 2152.97 6626.17i 0.102153 0.314395i
\(764\) 17082.7 + 52575.2i 0.808942 + 2.48967i
\(765\) 0 0
\(766\) 11196.7 34460.0i 0.528139 1.62545i
\(767\) 2230.38 + 1620.47i 0.104999 + 0.0762863i
\(768\) 0 0
\(769\) −1813.75 1317.77i −0.0850527 0.0617944i 0.544446 0.838796i \(-0.316740\pi\)
−0.629499 + 0.777001i \(0.716740\pi\)
\(770\) 29614.1 26226.3i 1.38600 1.22744i
\(771\) 0 0
\(772\) 48426.9 35184.2i 2.25767 1.64030i
\(773\) −10264.5 31590.8i −0.477604 1.46991i −0.842414 0.538831i \(-0.818866\pi\)
0.364810 0.931082i \(-0.381134\pi\)
\(774\) 0 0
\(775\) 19907.5 + 9259.21i 0.922708 + 0.429162i
\(776\) −4011.79 −0.185586
\(777\) 0 0
\(778\) 25514.6 18537.5i 1.17576 0.854243i
\(779\) 5024.13 3650.24i 0.231076 0.167886i
\(780\) 0 0
\(781\) −15129.3 10992.1i −0.693176 0.503622i
\(782\) −738.996 −0.0337934
\(783\) 0 0
\(784\) 47151.2 145116.i 2.14792 6.61062i
\(785\) 26039.2 2520.21i 1.18392 0.114586i
\(786\) 0 0
\(787\) −715.273 + 2201.38i −0.0323973 + 0.0997088i −0.965948